How to Micro Manage Manipulator
Enter Edit Mode, switch to Edge selection mode, select any edge, go to the Transform Orientations panel and press the + button to add a new transform orientation while that edge is selected.

You can name your new transform orientation whatever you want, and then use it afterwards. There will additionally be created a new transform orientation named "Edge" that will hold the orientation you want.

You can then move along that edge direction, or perpendicularly to it, relative to the surrounding faces normals.